Have seen a few studies and the opinion of most orthopedics docs is that single sport athletes are more prone to injury than multi sport athletes, for a couple basic reasons , overuse injuries and imbalance injuries as a result of building up more muscle etc. that is involved in your sport than muscle groups that may not be as involved.
I think in the younger grades maybe 8th and below it's great to play multiple sports. I don't know how, unless the kid is an off the meters freak athlete, a kid can develop and keep the skills needed to play multiple sports at a very high level. Football is the worst sport ever for severe injuries, that's just a fact.
Why is it that some of the coaches out there have this mentality that playing another sport makes you better at lacrosse? Do the basketball coaches at some colleges think by playing lacrosse you'll get better at basketball??? How about swimming, tennis, golf, soccer, cross country?? Do you become better at these sports by playing lacrosse? I don't think so. Top Basketball recruits play ball in season and AAU out of season. They don't play Lacrosse to get better. It is the most ridiculous notion that playing another sport is going to somehow endow you with more ability in another. Will it keep you in shape if you don't workout or train? sure. I think that's about it. If there was some measurable effect that made you better by playing another sport in the off season, surely college teams and even pro teams would have there athletes playing other sports. It's just the opposite, most high level college and pro teams what their players to refrain from playing other sports for fear of injury.